On the chromatic numbers of small-dimensional Euclidean spaces

On the chromatic numbers of small-dimensional Euclidean spaces

The paper is devoted to the study of graph sequence G_n = (V_n, E_n) where V_n is the set of all vectors v in R^n with coordinates from {-1, 0, 1} such that |v| = sqrt(3), and E_n consists of all pairs of vertices with the scalar product 1. We find exactly the independence number of G_n. As a coroll...

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Veröffentlicht in:arXiv.org 2016-08
Hauptverfasser: Cherkashin, Danila, Kulikov, Anatoly, Raigorodskii, Andrey
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Euclidean geometry
Lower bounds
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Zusammenfassung:The paper is devoted to the study of graph sequence G_n = (V_n, E_n) where V_n is the set of all vectors v in R^n with coordinates from {-1, 0, 1} such that |v| = sqrt(3), and E_n consists of all pairs of vertices with the scalar product 1. We find exactly the independence number of G_n. As a corollary we get some new lower bounds of chi(\R^n) and chi(\Q^n) for small values of n.
ISSN:2331-8422